Acoustic scattering from a fluid-elastic solid interface using the small slope approximation

Abstract

In this paper the small slope approximation is applied to acoustic scattering from a randomly rough fluid–elastic?solid interface. Expressions for the zeroth?, first?, and second?order bistatic scattering cross sections are derived. Numerical results are obtained for the zeroth?order small slope approximation for Gaussian and modified power law surface roughness spectra and are compared with those of first?order perturbation theory and the Kirchhoff approximation. The environmental parameters used correspond to those of water–granite, water–basalt, or water–sediment interfaces for lossless media. The small slope results show the complex structure associated with elastic wave scattering, including critical angle and Rayleigh angle structure. For the modified power law, the small slope results agree with those of Monte Carlo simulations performed by Berman [J. Acoust. Soc. Am. 89, 623–636 (1991)]. The study includes a comparison of scattering strengths both with and without the shear wave component. The importance of the shear wave component for a sufficiently rigid solid is illustrated.